{"abstract":[{"lang":"eng","text":"We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982."}],"issue":"1","title":"Kac's conjecture from Nakajima quiver varieties","extern":1,"page":"21 - 37","quality_controlled":0,"year":"2010","date_created":"2018-12-11T11:52:11Z","date_updated":"2021-01-12T06:50:56Z","status":"public","publication_status":"published","intvolume":"       181","publisher":"Springer","author":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas","full_name":"Tamas Hausel"}],"oa":1,"_id":"1465","publist_id":"5730","publication":"Inventiones Mathematicae","date_published":"2010-07-01T00:00:00Z","month":"07","day":"01","main_file_link":[{"url":"http://arxiv.org/abs/0811.1569","open_access":"1"}],"citation":{"ieee":"T. Hausel, “Kac’s conjecture from Nakajima quiver varieties,” <i>Inventiones Mathematicae</i>, vol. 181, no. 1. Springer, pp. 21–37, 2010.","short":"T. Hausel, Inventiones Mathematicae 181 (2010) 21–37.","ista":"Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37.","ama":"Hausel T. Kac’s conjecture from Nakajima quiver varieties. <i>Inventiones Mathematicae</i>. 2010;181(1):21-37. doi:<a href=\"https://doi.org/10.1007/s00222-010-0241-3\">10.1007/s00222-010-0241-3</a>","mla":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” <i>Inventiones Mathematicae</i>, vol. 181, no. 1, Springer, 2010, pp. 21–37, doi:<a href=\"https://doi.org/10.1007/s00222-010-0241-3\">10.1007/s00222-010-0241-3</a>.","apa":"Hausel, T. (2010). Kac’s conjecture from Nakajima quiver varieties. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-010-0241-3\">https://doi.org/10.1007/s00222-010-0241-3</a>","chicago":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” <i>Inventiones Mathematicae</i>. Springer, 2010. <a href=\"https://doi.org/10.1007/s00222-010-0241-3\">https://doi.org/10.1007/s00222-010-0241-3</a>."},"volume":181,"acknowledgement":"This work has been supported by a Royal Society University Research Fellowship, NSF grants DMS-0305505 and DMS-0604775 and an Alfred Sloan Fellowship 2005-2007.","doi":"10.1007/s00222-010-0241-3","type":"journal_article"}